The Unsolvability of The Quintic: A Case Study in Abstract Mathematical Explanation

Philosophers' Imprint 15 (2015)
  Copy   BIBTEX

Abstract

This paper identifies one way that a mathematical proof can be more explanatory than another proof. This is by invoking a more abstract kind of entity than the topic of the theorem. These abstract mathematical explanations are identified via an investigation of a canonical instance of modern mathematics: the Galois theory proof that there is no general solution in radicals for fifth-degree polynomial equations. I claim that abstract explanations are best seen as describing a special sort of dependence relation between distinct mathematical domains. This case study highlights the importance of the conceptual, as opposed to computational, turn of much of modern mathematics, as recently emphasized by Tappenden and Avigad. The approach adopted here is contrasted with alternative proposals by Steiner and Kitcher

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 93,127

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Analytics

Added to PP
2015-01-24

Downloads
101 (#176,983)

6 months
7 (#491,177)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Christopher Pincock
Ohio State University

Citations of this work

Viewing-as explanations and ontic dependence.William D’Alessandro - 2020 - Philosophical Studies 177 (3):769-792.
Mathematical Explanation beyond Explanatory Proof.William D’Alessandro - 2017 - British Journal for the Philosophy of Science 71 (2):581-603.

View all 16 citations / Add more citations

References found in this work

No references found.

Add more references